Research Topic

Our research topic is Trend of Major Types of Crimes commited by White Males in the DC Area in 2016-2021. We chose this topic because we are interested in the impact of COVID-19 on crimes. We will use the data provided by the Metropolitan Police of DC regarding adult arrests over a time period stretching between 2016-2021.

Data Shaping

Read Data

We read the data .CSV files of adults arrest in DC area from 2016-2021

df_2016<-data.frame(read.csv("Arrests 2016 Public.csv"))
df_2017<-data.frame(read.csv("Arrests 2017 Public.csv"))
df_2018<-data.frame(read.csv("Arrests by Year, 2018.csv"))
df_2019<-data.frame(read.csv("Arrests by Year, 2019.csv"))
df_2020<-data.frame(read.csv("Arrests by Year 2020.csv"))
df_2021<-data.frame(read.csv("2021 Adult Arrests.csv"))

c16 <- c(colnames(df_2016))
c18 <- c(colnames(df_2018))

The column names of the data in 2016 and 2017 were not the same with others. The below table shows the column names of the data in 2016 and the data in 2016.

col # 2016 2018
1 Arrestee.Type Arrestee.Type
2 Arrest.Year Arrest.Year
3 Arrest.Date Arrest.Date
4 Arrest.Hour Arrest.Hour
5 CCN CCN
6 Arrest.Number. Arrest.Number.
7 Age Age
8 Defendant.PSA Defendant.PSA
9 Defendant.District Defendant.District
10 Defendant.Race Defendant.Race
11 Defendant.Ethnicity Defendant.Ethnicity
12 Defendant.Sex Defendant.Sex
13 Arrest.Category Arrest.Category
14 Charge.Description Charge.Description
15 Arrest.Location.PSA Arrest.Location.PSA
16 Arrest.Location.District Arrest.Location.District
17 Arrest.Location.Block.GeoX Arrest.Block.GEOX
18 Arrest.Location.Block.GeoY Arrest.Block.GEOY
19 Offense.GEOY Arrest.Latitude
20 Offense.GEOX Arrest.Longitude
21 Offense.PSA Offense.Location.PSA
22 Offense.District Offense.Location.District
23 Arrest.Latitude Offense.Block.GEOX
24 Arrest.Longitude Offense.Block.GEOY
25 Offense.Latitude Offense.Latitude
26 Offense.Longitude Offense.Longitude

Merge Multiple CSV Files and Drop Some Columns

The column names were same from the first column to the 14th column in both data. On the other hand, the name and order of 15th and latter columns were a bit different in those data. The latter columns were about locations, and we were not very interested in the detail location. Therefore, we deleted the latter columns except for the 16th and 22nd columns. In addition, we dropped CNN (col #5) and Arrest.Number. (col #6) because they were IDs and useless for our analysis.

The format of date was different from years; the data in 2016 and 2017 has the format like , the data in 2018 to 2020 has the format like , and the data in 2021 has the format like . We coverted Since different date formats for different years are difficult to analyze, we will unify the date format to “yyyy-mm-dd”.

After deleting some columns and changing the date format, we binded data frames by rows.

# convert format
df_2018$Arrest.Date <- as.Date(df_2018$Arrest.Date, format = "%m/%d/%Y") %>% format()
df_2019$Arrest.Date <- as.Date(df_2019$Arrest.Date, format = "%m/%d/%Y") %>% format()
df_2020$Arrest.Date <- as.Date(df_2020$Arrest.Date, format = "%m/%d/%Y") %>% format()
df_2021$Arrest.Date <- as.Date(df_2021$Arrest.Date, format = "%Y/%m/%d") %>% format()

#bind df_2016 and df_2017, and delete some columns
df_16_17 <- rbind(df_2016, df_2017)[,-c(5,6,15,17:21,23:26)]
names(df_16_17)[c(13,14)] <- c('Arrest.Location.District','Offense.Location.District')   #rename columns

#bind df_2018 - df_2021, and delete some columns
df_18_21 <- rbind(df_2018, df_2019, df_2020, df_2021)[,-c(5,6,15,17:21,23:26)] 

DF<-rbind(df_16_17,df_18_21)

Correct Anomalies

Remove abnormal values

To see whether there were abnormal values, we created the table showing some statistics for numerical variables.

xkablesummary(subset(DF,select=c(Arrest.Year, Arrest.Hour, Age)))
Table: Statistics summary.
Arrest.Year Arrest.Hour Age
Min Min. :2016 Min. : 0.00 Min. : 18.00
Q1 1st Qu.:2017 1st Qu.: 6.00 1st Qu.: 25.00
Median Median :2018 Median :12.00 Median : 32.00
Mean Mean :2018 Mean :11.81 Mean : 35.19
Q3 3rd Qu.:2019 3rd Qu.:18.00 3rd Qu.: 43.00
Max Max. :2021 Max. :23.00 Max. :121.00

The maximum age was too old. 55 rows were assigned an age of over 100 years (117-121 ) in these data, and it seemed to be wrong. Therefore, we dropped these rows.

DF <- DF[!DF$Age>=100,]

Some data cleaning.. Dropping, Binding and Renaming of columns as needed.

# replace dots with underscore for clarity sake, i think..
names(DF) = gsub("[.]", "_", names(DF))
colnames(DF)
##  [1] "Arrestee_Type"             "Arrest_Year"              
##  [3] "Arrest_Date"               "Arrest_Hour"              
##  [5] "Age"                       "Defendant_PSA"            
##  [7] "Defendant_District"        "Defendant_Race"           
##  [9] "Defendant_Ethnicity"       "Defendant_Sex"            
## [11] "Arrest_Category"           "Charge_Description"       
## [13] "Arrest_Location_District"  "Offense_Location_District"
#find unique values in the race, sex and arrest_category columns.
#unique(DF$Defendant_Race)
#unique(DF$Defendant_Sex)
#unique(DF$Arrest_Category)

# most likely "UNK" is the same as "Unknown", so we can change this
DF$Defendant_Race[DF$Defendant_Race == 'UNK'] <- 'UNKNOWN'
#unique(DF$Defendant_Race) - check that it changed

#same issue, "unk" is very likely "unknown", so change it.
DF$Defendant_Sex[DF$Defendant_Sex == 'UNK'] <- 'UNKNOWN'
#unique(DF$Defendant_Sex) - check that it changed

# Arrest category -  4 different types of Fraud & Financial crimes , 3 types of Release Violations/Fugitive -- group them into one.

DF$Arrest_Category = gsub("Fraud and Financial Crimes.*","Fraud and Financial Crimes", DF$Arrest_Category)

DF$Arrest_Category = gsub("Release Violations/Fugitive.*","Release Violations/Fugitive",DF$Arrest_Category)

#sort(unique(DF$Arrest_Category)) - check that new changes were made.

Missing Values

sapply(DF, function(x) sum(is.na(x)))
##             Arrestee_Type               Arrest_Year               Arrest_Date 
##                         0                         0                         0 
##               Arrest_Hour                       Age             Defendant_PSA 
##                         0                         0                     29093 
##        Defendant_District            Defendant_Race       Defendant_Ethnicity 
##                      9337                         0                         0 
##             Defendant_Sex           Arrest_Category        Charge_Description 
##                         0                        12                        15 
##  Arrest_Location_District Offense_Location_District 
##                       184                        11
Our variables of concern in thsi dataset contain rich data.. over 95% of data available in each useful column.. will not delete any rows
#get month and day variables.. might be interesting, who knows?
DF <- separate(DF, col = Arrest_Date, into = c("Year","Month","Day"), sep = "-", remove = FALSE, fill="left")
#remove the new year column formed, it is redundant.. we already have Year column
DF = DF[,-4]
colnames(DF)
##  [1] "Arrestee_Type"             "Arrest_Year"              
##  [3] "Arrest_Date"               "Month"                    
##  [5] "Day"                       "Arrest_Hour"              
##  [7] "Age"                       "Defendant_PSA"            
##  [9] "Defendant_District"        "Defendant_Race"           
## [11] "Defendant_Ethnicity"       "Defendant_Sex"            
## [13] "Arrest_Category"           "Charge_Description"       
## [15] "Arrest_Location_District"  "Offense_Location_District"
library(lubridate)
## 
## Attaching package: 'lubridate'
## The following objects are masked from 'package:base':
## 
##     date, intersect, setdiff, union
# Factorize some variables
DF$Arrest_Year = as.factor(DF$Arrest_Year)
DF$Month = as.factor(DF$Month)
DF$Day = as.factor(DF$Day)
DF$Defendant_Race = as.factor(DF$Defendant_Race)
DF$Defendant_Sex = as.factor(DF$Defendant_Sex)
DF$Arrest_Location_District = as.factor(DF$Arrest_Location_District)
DF$Offense_Location_District = as.factor(DF$Offense_Location_District)
# convert to date format
DF$Arrest_Date = as.Date(DF$Arrest_Date)
# Day format
DF$Day = day(DF$Arrest_Date)
# i want to create a week-day variable
DF$Weekday = weekdays(DF$Arrest_Date)
DF$Weekday = factor(DF$Weekday, levels = as.character(wday(c(2:7,1), label=TRUE, abbr=FALSE)))

# convert crime types to factors
DF$Arrest_Category = as.factor(DF$Arrest_Category)

Correct inconsistent values

Arrest_Category had some different values for 2021 and other years:

  • Data in 2021 had “Release Violations/Fugitive (Fug)” and “Release Violations/Fugitive (Warr)” although data in other years have “Release Violations/Fugitive” instead of them.
  • Data in 2021 had “Fraud and Financial Crimes (Frau)” although data in other years have “Fraud and Financial Crimes”.

Therefore, we coverted these values in 2021 into the correspond values in other years.

DF <- mutate(DF, Arrest_Category = gsub(Arrest_Category, pattern = "Release Violations/Fugitive.*", replacement = "Release Violations/Fugitive"))
DF <- mutate(DF, Arrest_Category = gsub(Arrest_Category, pattern = "Fraud and Financial Crimes.*", replacement = "Fraud and Financial Crimes"))

Remove Unnecessary Rows

Since we were interested in crimes committed by while males, we dropped rows where the value of Defendant_Race was not “White”. The structure of the final data is shown in the below table.

DF_WM <- subset(DF, subset = Defendant_Race=='WHITE' & Defendant_Sex=='MALE')

data.frame(column_name = names(DF_WM),
           class = sapply(DF_WM, typeof),
           first_values = sapply(DF_WM, function(x) paste0(head(x),  collapse = ", ")),
           row.names = NULL) %>% 
  kable("simple", caption = 'Data frame structure')
Data frame structure
column_name class first_values
Arrestee_Type character Adult Arrest, Adult Arrest, Adult Arrest, Adult Arrest, Adult Arrest, Adult Arrest
Arrest_Year integer 2016, 2016, 2016, 2016, 2016, 2016
Arrest_Date double 2016-01-01, 2016-01-01, 2016-01-01, 2016-01-01, 2016-01-01, 2016-01-01
Month integer 01, 01, 01, 01, 01, 01
Day integer 1, 1, 1, 1, 1, 1
Arrest_Hour integer 0, 0, 1, 1, 13, 2
Age integer 39, 27, 27, 26, 48, 25
Defendant_PSA character Out of State, Out of State, Out of State, Out of State, 404, Out of State
Defendant_District character Out of State, Out of State, Out of State, Out of State, 4D, Out of State
Defendant_Race integer WHITE, WHITE, WHITE, WHITE, WHITE, WHITE
Defendant_Ethnicity character UNKNOWN, NOT HISPANIC, HISPANIC, NOT HISPANIC, NOT HISPANIC, HISPANIC
Defendant_Sex integer MALE, MALE, MALE, MALE, MALE, MALE
Arrest_Category character Simple Assault, Simple Assault, Driving/Boating While Intoxicated, Simple Assault, Simple Assault, Simple Assault
Charge_Description character Threats To Do Bodily Harm -misd, Simple Assault, Driving While Intoxicated -2nd Off, Simple Assault, Simple Assault, Simple Assault
Arrest_Location_District integer 2D, 3D, 4D, 5D, 1D, 3D
Offense_Location_District integer 2D, 3D, 4D, 5D, 1D, 3D
Weekday integer Friday, Friday, Friday, Friday, Friday, Friday

EDA

Crimes Committed by All

Hour of the day.. at what time do these crimes occur the most?

by_hour <- DF %>% 
           group_by(Arrest_Hour) %>% 
           dplyr::summarise(Total = n())
by_hour
## # A tibble: 24 × 2
##    Arrest_Hour Total
##          <int> <int>
##  1           0  5681
##  2           1  7425
##  3           2  6769
##  4           3  6286
##  5           4  5425
##  6           5  4412
##  7           6  4465
##  8           7  6101
##  9           8  6729
## 10           9  6594
## # … with 14 more rows
ggplot(by_hour, aes(Arrest_Hour, Total, color = Arrest_Hour)) + 
    geom_line() + 
    ggtitle("Crimes By Hour") + 
    xlab("Hour of the Day") + 
    ylab("Total Crimes")

Day .. What day of the month has the highest crime incidents?

by_day <- DF %>% 
           group_by(Day) %>% 
           dplyr::summarise(Total = n())
by_day
## # A tibble: 31 × 2
##      Day Total
##    <int> <int>
##  1     1  5516
##  2     2  5193
##  3     3  5240
##  4     4  5138
##  5     5  5189
##  6     6  4998
##  7     7  4878
##  8     8  5022
##  9     9  4947
## 10    10  5090
## # … with 21 more rows
ggplot(by_day, aes(Day, Total, color = Day)) + 
    geom_line() + 
    ggtitle("Crimes By Day") + 
    xlab("Day of the Month") + 
    ylab("Total Crimes")

Day of the week..

by_weekday = DF %>% group_by(Weekday) %>% 
           dplyr::summarise(Total = n())
by_weekday$Percent <- by_weekday$Total/dim(DF)[1] * 100
by_weekday
## # A tibble: 7 × 3
##   Weekday   Total Percent
##   <fct>     <int>   <dbl>
## 1 Monday    19553    12.8
## 2 Tuesday   21418    14.1
## 3 Wednesday 23520    15.4
## 4 Thursday  23241    15.3
## 5 Friday    23189    15.2
## 6 Saturday  22142    14.5
## 7 Sunday    19268    12.6
ggplot(by_weekday, aes(Weekday, Total, fill = Weekday)) + 
      geom_bar(stat = "identity") +
      ggtitle("Crimes By Weekday ") + 
      xlab("Day of the Week") + ylab("Count") + 
      theme(legend.position = "none")

Monthly crime incidence

by_month <- DF %>% 
            group_by(Month) %>% 
            dplyr::summarise(Total = n())

by_month$Percent <- by_month$Total/dim(DF)[1] * 100
by_month
## # A tibble: 12 × 3
##    Month Total Percent
##    <fct> <int>   <dbl>
##  1 01    12751    8.37
##  2 02    12158    7.98
##  3 03    13625    8.94
##  4 04    12344    8.10
##  5 05    13427    8.81
##  6 06    12729    8.36
##  7 07    13008    8.54
##  8 08    12991    8.53
##  9 09    12578    8.26
## 10 10    13029    8.55
## 11 11    11869    7.79
## 12 12    11822    7.76
#ggplot(by_month, aes(Month, Total, fill = Month)) + 
        #geom_bar(stat = "identity") + 
        #ggtitle("Crimes By Month") + 
        #xlab("Month") + 
        #ylab("Count") + 
        #theme(legend.position = "none")

ggplot(by_month, aes(x=Month, y=Total, group=1)) + geom_line()

Crime incidence grouped into yearly plots..

by_year = DF %>% group_by(Arrest_Year) %>% 
           dplyr::summarise(Total = n())
by_year$Percent <- by_year$Total/dim(DF)[1] * 100
by_year
## # A tibble: 6 × 3
##   Arrest_Year Total Percent
##   <fct>       <int>   <dbl>
## 1 2016        29980    19.7
## 2 2017        31209    20.5
## 3 2018        29100    19.1
## 4 2019        27915    18.3
## 5 2020        18479    12.1
## 6 2021        15648    10.3
#ggplot(by_year, aes(Arrest_Year, Total, fill = Arrest_Year)) + 
      #geom_bar(stat = "identity") +
      #ggtitle("Crimes By Year ") + 
      #xlab("Year") + ylab("Count") + 
      #theme(legend.position = "none")

ggplot(by_year, aes(x=Arrest_Year, y=Total, group=1)) + geom_line()

Some Boxplots

PADM = ggplot(DF, aes(group = factor(Arrest_Year), y = Age,x= Arrest_Year, fill = factor(Arrest_Year))) + 
  geom_boxplot() + 
  geom_boxplot(outlier.shape=8, outlier.size=5) +
  labs(title="Age VS Year", x="Year", y = "Age")
PADM

This plot is to compare the age of people who get arrested with each different year. From the plot, we can see that there are lots of outliers. We need to get rid of the outliers first.

Q1 = quantile(DF$Age, .25)
Q3 = quantile(DF$Age, .75)
IQR = IQR(DF$Age)

#only keep rows in dataframe that have values within 1.5*IQR of Q1 and Q3
ndf = subset(DF, DF$Age> (Q1 - 1.5*IQR) & DF$Age< (Q3 + 1.5*IQR))

#view row and column count of new data frame
dim(ndf) 
## [1] 151552     17
dim(DF)
## [1] 152331     17

Removed 834 outliers.

ATY = ggplot(ndf, aes(group = factor(Arrest_Year), y = Age, x= Arrest_Year, fill = factor(Arrest_Year))) + 
  geom_boxplot() + 
  geom_boxplot(outlier.shape=8, outlier.size=5) +
  labs(title="Age VS Year", x="Year", y = "Age")
ATY

After remove the ourliers, we could clearly see that as year goes up, the minimum age goes up a little bit. The maximum age from this sample goes down. The median is pretty much same compare to different years.

There are less younger criminals as year passing from 2016 to 2020 based on this sample. Criminal with age from 30 to 35 arrested more than other ages, which also probably means that there are more offenders with age from 30 to 35.

Why boxplot? The advantage of consider median over sample mean is that it is less affected by extreme observations.

unique(DF$Defendant_Race)
## [1] WHITE    BLACK    UNKNOWN  ASIAN    MULTIPLE OTHER   
## Levels: ASIAN BLACK MULTIPLE OTHER UNKNOWN WHITE
rrw = sum(DF$Defendant_Race == "WHITE")
rrb = sum(DF$Defendant_Race == "BLACK")
rra = sum(DF$Defendant_Race == "ASIAN")
rrw
## [1] 15739
rrb
## [1] 131385
rra
## [1] 897
unique(DF$Arrest_Category)
##  [1] "Simple Assault"                     "Assault on a Police Officer"       
##  [3] "Traffic Violations"                 "Weapon Violations"                 
##  [5] "Driving/Boating While Intoxicated"  "Narcotics"                         
##  [7] "Disorderly Conduct"                 "Theft"                             
##  [9] "Liquor Law Violations"              "Other Crimes"                      
## [11] "Theft from Auto"                    "Offenses Against Family & Children"
## [13] "Assault with a Dangerous Weapon"    "Release Violations/Fugitive"       
## [15] "Motor Vehicle Theft"                "Damage to Property"                
## [17] "Sex Abuse"                          "Property Crimes"                   
## [19] "Vending Violations"                 "Robbery"                           
## [21] "Aggravated Assault"                 "Burglary"                          
## [23] "Sex Offenses"                       "Fraud and Financial Crimes"        
## [25] "Prostitution"                       "Homicide"                          
## [27] "Kidnapping"                         "Gambling"                          
## [29] "Arson"                              NA
ss = subset(DF,DF$Arrest_Category == "Sex Abuse")
HH = ggplot(ss, aes(group = factor(Arrest_Year), y = Arrest_Hour,x= Arrest_Year, fill = factor(Arrest_Year))) + 
  geom_boxplot() + 
  geom_boxplot(outlier.shape=8, outlier.size=5) +
  labs(title="Arrest_Hour VS Year", x="Year", y = "Arrest_Hour")
HH

From the box plot, we can see that most sex abuse happens around 10am to 13pm. The sex abuse happens all the time and it changes with different years.

tt = subset(DF,DF$Arrest_Category == "Theft")
HHH = ggplot(tt, aes(group = factor(Arrest_Year), y = Arrest_Hour,x= Arrest_Year, fill = factor(Arrest_Year))) + 
  geom_boxplot() + 
  geom_boxplot(outlier.shape=8, outlier.size=5) +
  labs(title="Arrest_Hour VS Year", x="Year", y = "Arrest_Hour")
HHH

From the box plot, we can see that most theft happens around 15pm and they all super same with each year except year 2019. The theft always happening from 11am to 19 pm. That’s a funny fact.

Crimes Committed by White Male

### Time to investigate our main focus group - White Males - EDA
#unique(DF$Defendant_Race)
#table(DF$Defendant_Sex)
df_wm = subset(DF, subset = Defendant_Race == "WHITE" & Defendant_Sex == "MALE")
head(df_wm, 20)
##     Arrestee_Type Arrest_Year Arrest_Date Month Day Arrest_Hour Age
## 1    Adult Arrest        2016  2016-01-01    01   1           0  39
## 2    Adult Arrest        2016  2016-01-01    01   1           0  27
## 12   Adult Arrest        2016  2016-01-01    01   1           1  27
## 14   Adult Arrest        2016  2016-01-01    01   1           1  26
## 24   Adult Arrest        2016  2016-01-01    01   1          13  48
## 54   Adult Arrest        2016  2016-01-01    01   1           2  25
## 76   Adult Arrest        2016  2016-01-01    01   1           3  21
## 84   Adult Arrest        2016  2016-01-01    01   1           3  41
## 96   Adult Arrest        2016  2016-01-01    01   1           6  29
## 98   Adult Arrest        2016  2016-01-01    01   1           7  22
## 104  Adult Arrest        2016  2016-01-02    01   2           0  51
## 110  Adult Arrest        2016  2016-01-02    01   2           1  29
## 114  Adult Arrest        2016  2016-01-02    01   2          11  64
## 123  Adult Arrest        2016  2016-01-02    01   2          15  33
## 131  Adult Arrest        2016  2016-01-02    01   2          16  23
## 138  Adult Arrest        2016  2016-01-02    01   2          17  49
## 161  Adult Arrest        2016  2016-01-02    01   2          21  30
## 171  Adult Arrest        2016  2016-01-02    01   2           3  22
## 175  Adult Arrest        2016  2016-01-02    01   2           4  28
## 194  Adult Arrest        2016  2016-01-03    01   3          15  27
##     Defendant_PSA Defendant_District Defendant_Race Defendant_Ethnicity
## 1    Out of State       Out of State          WHITE             UNKNOWN
## 2    Out of State       Out of State          WHITE        NOT HISPANIC
## 12   Out of State       Out of State          WHITE            HISPANIC
## 14   Out of State       Out of State          WHITE        NOT HISPANIC
## 24            404                 4D          WHITE        NOT HISPANIC
## 54   Out of State       Out of State          WHITE            HISPANIC
## 76   Out of State       Out of State          WHITE            HISPANIC
## 84            307                 3D          WHITE            HISPANIC
## 96   Out of State       Out of State          WHITE            HISPANIC
## 98            402                 4D          WHITE            HISPANIC
## 104  Out of State       Out of State          WHITE        NOT HISPANIC
## 110  Out of State       Out of State          WHITE            HISPANIC
## 114  Out of State       Out of State          WHITE             UNKNOWN
## 123           302                 3D          WHITE            HISPANIC
## 131           506                 5D          WHITE            HISPANIC
## 138  Out of State       Out of State          WHITE            HISPANIC
## 161  Out of State       Out of State          WHITE        NOT HISPANIC
## 171  Out of State       Out of State          WHITE            HISPANIC
## 175           201                 2D          WHITE        NOT HISPANIC
## 194           403                 4D          WHITE            HISPANIC
##     Defendant_Sex                   Arrest_Category
## 1            MALE                    Simple Assault
## 2            MALE                    Simple Assault
## 12           MALE Driving/Boating While Intoxicated
## 14           MALE                    Simple Assault
## 24           MALE                    Simple Assault
## 54           MALE                    Simple Assault
## 76           MALE             Liquor Law Violations
## 84           MALE Driving/Boating While Intoxicated
## 96           MALE                    Simple Assault
## 98           MALE                    Simple Assault
## 104          MALE       Release Violations/Fugitive
## 110          MALE                Traffic Violations
## 114          MALE                    Simple Assault
## 123          MALE   Assault with a Dangerous Weapon
## 131          MALE                 Weapon Violations
## 138          MALE             Liquor Law Violations
## 161          MALE                         Narcotics
## 171          MALE                    Simple Assault
## 175          MALE                Damage to Property
## 194          MALE                Traffic Violations
##                                        Charge_Description
## 1                         Threats To Do Bodily Harm -misd
## 2                                          Simple Assault
## 12                     Driving While Intoxicated -2nd Off
## 14                                         Simple Assault
## 24                                         Simple Assault
## 54                                         Simple Assault
## 76  Poss Of Open Container Of Alcohol/public Intoxication
## 84                       Driving Under Influence -2nd Off
## 96                                         Simple Assault
## 98                                         Simple Assault
## 104                              Failure To Appear (USAO)
## 110                                             No Permit
## 114                                        Simple Assault
## 123                       Assault With A Dangerous Weapon
## 131                             Possess Prohibited Weapon
## 138     Possession Of An Open Container Of Alcohol (poca)
## 161               Poss W/i To Dist A Controlled Substance
## 171                                        Simple Assault
## 175               Destruction Of Property Less Than $1000
## 194                                             No Permit
##     Arrest_Location_District Offense_Location_District  Weekday
## 1                         2D                        2D   Friday
## 2                         3D                        3D   Friday
## 12                        4D                        4D   Friday
## 14                        5D                        5D   Friday
## 24                        1D                        1D   Friday
## 54                        3D                        3D   Friday
## 76                        2D                        2D   Friday
## 84                        2D                        2D   Friday
## 96                        2D                        2D   Friday
## 98                        4D                        4D   Friday
## 104                       4D                        1D Saturday
## 110                       4D                        4D Saturday
## 114                       2D                        2D Saturday
## 123                       4D                        4D Saturday
## 131                       5D                        5D Saturday
## 138                       3D                        3D Saturday
## 161                       1D                        1D Saturday
## 171                       2D                        2D Saturday
## 175                       3D                        3D Saturday
## 194                       4D                        4D   Sunday
# i want to create a week-day variable
df_wm$Weekday = weekdays(df_wm$Arrest_Date)
df_wm$Weekday = factor(df_wm$Weekday, levels = as.character(wday(c(2:7,1), label=TRUE, abbr=FALSE)))

same pattern here as above, will dig into a few other stuff too..

White Men - By the Hour

wm_by_hour <- df_wm %>% 
           group_by(Arrest_Hour) %>% 
           dplyr::summarise(Total = n())
wm_by_hour
## # A tibble: 24 × 2
##    Arrest_Hour Total
##          <int> <int>
##  1           0   605
##  2           1   801
##  3           2   813
##  4           3   695
##  5           4   552
##  6           5   329
##  7           6   322
##  8           7   405
##  9           8   424
## 10           9   442
## # … with 14 more rows
ggplot(wm_by_hour, aes(Arrest_Hour, Total, color = Arrest_Hour)) + 
    geom_line() + 
    ggtitle("White Males - Crimes By Hour") + 
    xlab("Hour of the Day") + 
    ylab("Total Crimes")

White Men - What day of the month has the highest crime incidents?

wm_by_day <- df_wm %>% 
           group_by(Day) %>% 
           dplyr::summarise(Total = n())
wm_by_day
## # A tibble: 31 × 2
##      Day Total
##    <int> <int>
##  1     1   524
##  2     2   404
##  3     3   403
##  4     4   395
##  5     5   405
##  6     6   455
##  7     7   405
##  8     8   376
##  9     9   399
## 10    10   430
## # … with 21 more rows
ggplot(wm_by_day, aes(Day, Total, color = Day)) + 
    geom_line() + 
    ggtitle("White Males - Crimes By Day") + 
    xlab("Day of the Month") + 
    ylab("Total Crimes")

White Men - What Day of the Week has the highest crime incidents?

wm_by_weekday = df_wm %>% group_by(Weekday) %>% 
           dplyr::summarise(Total = n())
wm_by_weekday$Percent <- wm_by_weekday$Total/dim(df_wm)[1] * 100
wm_by_weekday
## # A tibble: 7 × 3
##   Weekday   Total Percent
##   <fct>     <int>   <dbl>
## 1 Monday     1566    12.8
## 2 Tuesday    1463    11.9
## 3 Wednesday  1639    13.3
## 4 Thursday   1736    14.1
## 5 Friday     1876    15.3
## 6 Saturday   2046    16.7
## 7 Sunday     1952    15.9
ggplot(wm_by_weekday, aes(Weekday, Total, fill = Weekday)) + 
      geom_bar(stat = "identity") +
      ggtitle("White Males - Crimes By Weekday ") + 
      xlab("Day of the Week") + ylab("Count") + 
      theme(legend.position = "none")

White Males - By Month

wm_by_month <- df_wm %>% 
            group_by(Month) %>% 
            dplyr::summarise(Total = n())

wm_by_month$Percent <- wm_by_month$Total/dim(df_wm)[1] * 100
wm_by_month
## # A tibble: 12 × 3
##    Month Total Percent
##    <fct> <int>   <dbl>
##  1 01     1189    9.68
##  2 02      998    8.13
##  3 03     1125    9.16
##  4 04      921    7.50
##  5 05     1058    8.62
##  6 06     1010    8.23
##  7 07      966    7.87
##  8 08      961    7.83
##  9 09     1023    8.33
## 10 10     1108    9.02
## 11 11      991    8.07
## 12 12      928    7.56
ggplot(wm_by_month, aes(Month, Total, fill = Month)) + 
        geom_bar(stat = "identity") + 
        ggtitle("White Males - Crimes By Month") + 
        xlab("Month") + 
        ylab("Count") + 
        theme(legend.position = "none")

ggplot(wm_by_month, aes(x=Month, y=Total, group=1)) + geom_line()

White Men - Yearly Crime Incidents

wm_by_year = df_wm %>% group_by(Arrest_Year) %>% 
           dplyr::summarise(Total = n())
wm_by_year$Percent <- wm_by_year$Total/dim(df_wm)[1] * 100
wm_by_year
## # A tibble: 6 × 3
##   Arrest_Year Total Percent
##   <fct>       <int>   <dbl>
## 1 2016         2620   21.3 
## 2 2017         2636   21.5 
## 3 2018         2297   18.7 
## 4 2019         2191   17.8 
## 5 2020         1425   11.6 
## 6 2021         1109    9.03
ggplot(wm_by_year, aes(Arrest_Year, Total, fill = Arrest_Year)) + 
      geom_bar(stat = "identity") +
      ggtitle("White Males - Crimes By Year ") + 
      xlab("Year") + ylab("Count") + 
      theme(legend.position = "none")

ggplot(wm_by_year, aes(x=Arrest_Year, y=Total, group=1)) + geom_line()

Let us get into crime types…

wm_by_cat <- df_wm %>% 
          group_by(Arrest_Category) %>% 
          dplyr::summarise(Total = n()) %>% 
          arrange(desc(Total))

wm_by_cat[1:10,]
## # A tibble: 10 × 2
##    Arrest_Category                   Total
##    <chr>                             <int>
##  1 Simple Assault                     2661
##  2 Traffic Violations                 1548
##  3 Release Violations/Fugitive        1133
##  4 Driving/Boating While Intoxicated  1045
##  5 Other Crimes                        821
##  6 Theft                               674
##  7 Narcotics                           654
##  8 Liquor Law Violations               562
##  9 Disorderly Conduct                  433
## 10 Damage to Property                  414
ggplot(wm_by_cat, aes(reorder(Arrest_Category, Total), Total)) + 
    geom_bar(stat = "identity") + coord_flip() +  
    scale_y_continuous(breaks = seq(0,3000,500)) + 
    ggtitle("Crimes By Arrest Category") + 
    xlab("Crime Type") + 
    ylab("Number of Incidents")

wm_by_cat_year <- df_wm %>% group_by(Arrest_Year, Arrest_Category) %>% 
                dplyr::summarise(Total = n())
## `summarise()` has grouped output by 'Arrest_Year'. You can override using the
## `.groups` argument.
wm_by_cat_year[1:10,]
## # A tibble: 10 × 3
## # Groups:   Arrest_Year [1]
##    Arrest_Year Arrest_Category                   Total
##    <fct>       <chr>                             <int>
##  1 2016        Aggravated Assault                   23
##  2 2016        Assault on a Police Officer          42
##  3 2016        Assault with a Dangerous Weapon      73
##  4 2016        Burglary                             25
##  5 2016        Damage to Property                   98
##  6 2016        Disorderly Conduct                   83
##  7 2016        Driving/Boating While Intoxicated   206
##  8 2016        Fraud and Financial Crimes           11
##  9 2016        Homicide                              2
## 10 2016        Kidnapping                            4
ggplot(wm_by_cat_year, aes(reorder(Arrest_Category, Total), Total, fill = Arrest_Year)) + 
    geom_bar(stat = "identity") + 
    scale_y_continuous(breaks = seq(0,3000,500)) + 
    coord_flip() + ggtitle("Crimes By Code and Year") + 
    xlab("Crime Text Code") + 
    ylab("Total Crimes")

Some Top Crimes

Location Stuff

unique(df_wm$Arrest_Location_District)
##  [1] 2D      3D      4D      5D      1D      7D      6D      UNKNOWN <NA>   
## [10]        
## Levels:  1D 2D 3D 4D 5D 6D 7D UNKNOWN
table(df_wm$Arrest_Location_District)
## 
##              1D      2D      3D      4D      5D      6D      7D UNKNOWN 
##      22    1858    3053    2555    2816    1231     437     260      29
unique(df_wm$Offense_Location_District)
##  [1] 2D      3D      4D      5D      1D      7D      6D      #N/A    UNKNOWN
## [10] Unk    
## Levels: #N/A 1D 2D 3D 4D 5D 6D 7D Unk UNKNOWN
table(df_wm$Offense_Location_District)
## 
##    #N/A      1D      2D      3D      4D      5D      6D      7D     Unk UNKNOWN 
##      12    2044    3100    2531    2719    1195     413     238      16      10
### drop the unknowns here .. they are few..
wm_by_ALD <- df_wm %>% group_by(Arrest_Location_District) %>% 
         dplyr::summarise(Total = n()) %>% 
         dplyr::arrange(desc(Total))
wm_by_ALD2 = wm_by_ALD[1:7,]

wm_by_OLD <- df_wm %>% group_by(Offense_Location_District) %>% 
         dplyr::summarise(Total = n()) %>% 
         dplyr::arrange(desc(Total))
wm_by_OLD2 = wm_by_OLD[1:7,]

ggplot(wm_by_ALD2, aes(reorder(Arrest_Location_District, -Total), Total)) + 
      geom_bar(stat = "identity") + 
      ggtitle("Crimes by Arrest Location District") + 
      xlab("Location District") + 
      ylab("Total Crimes") 

ggplot(wm_by_OLD2, aes(reorder(Offense_Location_District, -Total), Total)) + 
      geom_bar(stat = "identity") + 
      ggtitle("Crimes by Offense Location District") + 
      xlab("Location District") + 
      ylab("Total Crimes") 

# top 5 crimes in each district
#ALD_dc_top7 <- wm_by_ALD$Arrest_Location_District[1:5]

#ALD_top7_dc <- subset(df_wm, Arrest_Location_District %in% wm_by_ALD$Arrest_Location_District[1:5])
#ALD_top7_dc$Arrest_Location_District <- factor(ALD_top7_dc$Arrest_Location_District)

#ggplot(ALD_top7_dc, aes(Arrest_Category, fill = Arrest_Location_District)) + 
      #geom_bar(position = "dodge") + 
      #ggtitle("Crimes by District Police HeadQuarters - Top 5") + 
      #xlab("Police HQ") + 
      #ylab("Total Crimes") 

#top crime by ARREST Location District 
ALD_by_crime <- df_wm  %>% 
      group_by(Arrest_Location_District, Arrest_Category) %>% 
      dplyr::summarise(Total = n()) %>% 
      arrange(desc(Total)) %>% top_n(n = 1)
## `summarise()` has grouped output by 'Arrest_Location_District'. You can
## override using the `.groups` argument.
## Selecting by Total
ALD_by_crime1 = ALD_by_crime[1:7,]

#dc_by_crime <- as.data.frame(dc_by_crime)
#dc_by_crime$Dc_Dist <- factor(dc_by_crime$Dc_Dist)
#dc_by_crime$Text_General_Code <- factor(dc_by_crime$Text_General_Code)

ggplot(ALD_by_crime1, aes(Arrest_Location_District, Total, fill = Arrest_Category)) + 
      geom_bar(stat = "identity") + 
      ggtitle("Top Crime by Arrest Location District") + 
      xlab("Location District") + 
      ylab("Total") 

#top crime by OFFENSE Location District
OLD_by_crime <- df_wm  %>% 
      group_by(Offense_Location_District, Arrest_Category) %>% 
      dplyr::summarise(Total = n()) %>% 
      arrange(desc(Total)) %>% top_n(n = 1)
## `summarise()` has grouped output by 'Offense_Location_District'. You can
## override using the `.groups` argument.
## Selecting by Total
OLD_by_crime1 = OLD_by_crime[1:7,]

#dc_by_crime <- as.data.frame(dc_by_crime)
#dc_by_crime$Dc_Dist <- factor(dc_by_crime$Dc_Dist)
#dc_by_crime$Text_General_Code <- factor(dc_by_crime$Text_General_Code)

ggplot(OLD_by_crime1, aes(Offense_Location_District, Total, fill = Arrest_Category)) + 
      geom_bar(stat = "identity") + 
      ggtitle("Top Crime by Offense Location District") + 
      xlab("Location District") + 
      ylab("Total")

Number of Each Crime

We created some bar plots to see the number of occurrences per type of crime.
The Bar plots of crimes in each year are as follows:

ggplot(subset(DF_WM,Arrest_Year == 2016), aes(forcats::fct_infreq(Arrest_Category))) +
  ggtitle("Figure 4: Bar plot of crimes in 2016") + xlab("crime types") + geom_bar() +
  theme(axis.text.x = element_text(angle = 60, hjust = 1))

ggplot(subset(DF_WM,Arrest_Year == 2017), aes(forcats::fct_infreq(Arrest_Category))) +
  ggtitle("Figure 5: Bar plot of crimes in 2017") + xlab("crime types") + geom_bar() +
  theme(axis.text.x = element_text(angle = 60, hjust = 1))

ggplot(subset(DF_WM,Arrest_Year == 2018), aes(forcats::fct_infreq(Arrest_Category))) +
  ggtitle("Figure 6: Bar plot of crimes in 2018") + xlab("crime types") + geom_bar() +
  theme(axis.text.x = element_text(angle = 60, hjust = 1))

ggplot(subset(DF_WM,Arrest_Year == 2019), aes(forcats::fct_infreq(Arrest_Category))) +
  ggtitle("Figure 7: Bar plot of crimes in 2019") + xlab("crime types") + geom_bar() +
  theme(axis.text.x = element_text(angle = 60, hjust = 1))

ggplot(subset(DF_WM,Arrest_Year == 2020), aes(forcats::fct_infreq(Arrest_Category))) +
  ggtitle("Figure 8: Bar plot of crimes in 2020") + xlab("crime types") + geom_bar() +
  theme(axis.text.x = element_text(angle = 60, hjust = 1))

ggplot(subset(DF_WM,Arrest_Year == 2021), aes(forcats::fct_infreq(Arrest_Category))) +
  ggtitle("Figure 9: Bar plot of crimes in 2021") + xlab("crime types") + geom_bar() +
  theme(axis.text.x = element_text(angle = 60, hjust = 1))

“Offenses Against Family & Children” have been increasing after COVD-19.

cnt_2016 <- table(subset(DF_WM,Arrest_Year==2016)$Arrest_Category)
pos_2016 <- order(cnt_2016, decreasing = TRUE)[1:6]
crime_2016 <- names(cnt_2016)[pos_2016]

cnt_2017 <- table(subset(DF_WM,Arrest_Year==2017)$Arrest_Category)
pos_2017 <- order(cnt_2017, decreasing = TRUE)[1:7]
crime_2017 <- names(cnt_2017)[pos_2017]

cnt_2018 <- table(subset(DF_WM,Arrest_Year==2018)$Arrest_Category)
pos_2018 <- order(cnt_2018, decreasing = TRUE)[1:6]
crime_2018 <- names(cnt_2018)[pos_2018]

cnt_2019 <- table(subset(DF_WM,Arrest_Year==2019)$Arrest_Category)
pos_2019 <- order(cnt_2019, decreasing = TRUE)[1:7]
crime_2019 <- names(cnt_2019)[pos_2019]

cnt_2020 <- table(subset(DF_WM,Arrest_Year==2020)$Arrest_Category)
pos_2020 <- order(cnt_2020, decreasing = TRUE)[1:7]
crime_2020 <- names(cnt_2020)[pos_2020]

cnt_2021 <- table(subset(DF_WM,Arrest_Year==2021)$Arrest_Category)
pos_2021 <- order(cnt_2021, decreasing = TRUE)[1:7]
crime_2021 <- names(cnt_2021)[pos_2021]

The top 6 crimes (or 7 crimes when ‘Other Crimes’ are included) in each year are as follows.

Rank 2016 2017 2018 2019 2020 2021
1 Simple Assault Simple Assault Simple Assault Simple Assault Simple Assault Simple Assault
2 Traffic Violations Traffic Violations Traffic Violations Traffic Violations Driving/Boating While Intoxicated Traffic Violations
3 Release Violations/Fugitive Release Violations/Fugitive Release Violations/Fugitive Prostitution Release Violations/Fugitive Driving/Boating While Intoxicated
4 Driving/Boating While Intoxicated Driving/Boating While Intoxicated Driving/Boating While Intoxicated Driving/Boating While Intoxicated Traffic Violations Release Violations/Fugitive
5 Liquor Law Violations Other Crimes Narcotics Release Violations/Fugitive Offenses Against Family & Children Other Crimes
6 Narcotics Disorderly Conduct Theft Other Crimes Other Crimes Offenses Against Family & Children
7 NA Liquor Law Violations NA Theft Narcotics Damage to Property

Time Series Change in the Number of Major Crimes

To see the trend of the above major crimes, we created a line plot as follows.

SA_cnt <- sapply(unique(DF_WM[DF_WM$Arrest_Category=='Simple Assault',]$Arrest_Year),
                       function(x){sum(DF_WM[DF_WM$Arrest_Category=='Simple Assault',]$Arrest_Year==x)})
TV_cnt <- sapply(unique(DF_WM[DF_WM$Arrest_Category=='Traffic Violations',]$Arrest_Year),
                       function(x){sum(DF_WM[DF_WM$Arrest_Category=='Traffic Violations',]$Arrest_Year==x)})
RV_cnt <- sapply(unique(DF_WM[DF_WM$Arrest_Category=='Release Violations/Fugitive',]$Arrest_Year),
                       function(x){sum(DF_WM[DF_WM$Arrest_Category=='Release Violations/Fugitive',]$Arrest_Year==x)})
DI_cnt <- sapply(unique(DF_WM[DF_WM$Arrest_Category=='Driving/Boating While Intoxicated',]$Arrest_Year),
                       function(x){sum(DF_WM[DF_WM$Arrest_Category=='Driving/Boating While Intoxicated',]$Arrest_Year==x)})
N_cnt <- sapply(unique(DF_WM[DF_WM$Arrest_Category=='Narcotics',]$Arrest_Year),
                       function(x){sum(DF_WM[DF_WM$Arrest_Category=='Narcotics',]$Arrest_Year==x)})
LV_cnt <- sapply(unique(DF_WM[DF_WM$Arrest_Category=='Liquor Law Violations',]$Arrest_Year),
                       function(x){sum(DF_WM[DF_WM$Arrest_Category=='Liquor Law Violations',]$Arrest_Year==x)})
T_cnt <- sapply(unique(DF_WM[DF_WM$Arrest_Category=='Theft',]$Arrest_Year),
                       function(x){sum(DF_WM[DF_WM$Arrest_Category=='Theft',]$Arrest_Year==x)})
DV_cnt <- sapply(unique(DF_WM[DF_WM$Arrest_Category=='Offenses Against Family & Children',]$Arrest_Year),
                       function(x){sum(DF_WM[DF_WM$Arrest_Category=='Offenses Against Family & Children',]$Arrest_Year==x)})
DC_cnt <- sapply(unique(DF_WM[DF_WM$Arrest_Category=='Disorderly Conduct',]$Arrest_Year),
                       function(x){sum(DF_WM[DF_WM$Arrest_Category=='Disorderly Conduct',]$Arrest_Year==x)})
P_cnt <- sapply(unique(DF_WM[DF_WM$Arrest_Category=='Prostitution',]$Arrest_Year),
                       function(x){sum(DF_WM[DF_WM$Arrest_Category=='Prostitution',]$Arrest_Year==x)})
DP_cnt <- sapply(unique(DF_WM[DF_WM$Arrest_Category=='Damage to Property',]$Arrest_Year),
                       function(x){sum(DF_WM[DF_WM$Arrest_Category=='Damage to Property',]$Arrest_Year==x)})
year_lst <- 2016:2021

major_crimes_df <- data.frame(year_lst, SA_cnt, TV_cnt, RV_cnt, DI_cnt, N_cnt, LV_cnt, T_cnt, DV_cnt, DC_cnt, P_cnt, DP_cnt)

colnames(major_crimes_df) <- c('Year', 'Simple Assault', 'Traffic Violations', 'Release Violations/Fugitive', 'Driving/Boating While Intoxicated',
                               'Narcotics', 'Liquor Law Violations', 'Theft', 'Offenses Against Family & Children', 'Disorderly Conduct', 'Prostitution', 'Damage to Property')

major_crimes_df2 <- major_crimes_df %>% gather(key = 'Crimes', value = "Count", -Year)

ggplot(data=major_crimes_df2, aes(x=Year, y=Count, color=Crimes)) +
  geom_line() + geom_point()

“Simple Assault”, “Traffic Violations”, and “Theft” have clearly declined since 2020. On the other, “Offenses Against Family & Children” has increased in 2020 and 2021 compared to previous years. COVID-19 seems to be related to these trend change. We posed the following SMART QUESTION, and we will analyze these four crimes in detail in the following.

Is there a significant difference in “Simple Assault”, “Traffic Violations”, “Theft”, and “Offenses Against Family & Children” trends among adult white males within the DC area between 2016 and 2021, and could COVID protocols play a role in these trend shifts?

Analysis

Since crime is likely to be a rare event, the number of occurrences per day of a given crime is expected to follow Poisson distribution. Poisson distribution is a distribution used to describe the distribution of the number of rare phenomena when a large number of them are observed. If a distribution follows Poisson distribution, and the average number of occurrences of the phenomenon is \(\lambda\), the probability that the phenomenon will occur \(x\) times is given by \[p(x) = \exp(-\lambda)\frac{\lambda^{x}}{x!}.\] In the following, we will estimate \(\lambda\) of each crime before and after COVID-19 to see there is a difference in crime trend.

Offenses Against Family & Children

Before COVID-19

The trend of “Offenses Against Family & Children,” Domestic Violence (DV), appears to have changed after COVID-19. The frequency table of DV before COVID-19 is as follows.

DF_WM_16_19 <- DF_WM[DF_WM$Arrest_Year%in%c(2016,2017,2018,2019),]
DF_WM_16_19_DV <- DF_WM_16_19[DF_WM_16_19$Arrest_Category=='Offenses Against Family & Children',]

# table of date and the number of occurrences
DV_day_16_19 <- sapply(unique(DF_WM_16_19_DV$Arrest_Date),
                       function(x){sum(DF_WM_16_19_DV$Arrest_Date==x)})
# of occurrences per day Frequency Relative frequency
0 1364 0.9336071
1 95 0.065024
2 2 0.0013689
3 0 0

We can calculate \(\lambda\) from the above table and \(\lambda = 0.0678\). We will plot the histogram and Poisson distribution with \(\lambda = 0.0678\) to check if they match or not.

x_DV <- 0:5
y_DV <- c(1364,95,2,0,0,0)
fx <- dpois(x=x_DV, lambda=99/(365*4+1))
data_DV <- data.frame(x_DV, y_DV, fx)

ggplot(data_DV, aes(x=x_DV,y=y_DV)) +
  ggtitle("Figure 13: Histogram of DV in 2016 - 2019") + 
  xlab("Number of occurrences per day") + 
  ylab("Frequency") +
  geom_bar(stat = "identity") 

ggplot(data_DV) +
  ggtitle("Figure 14: Relative frequency histogram of DV in 2016 - 2019 \n and Poisson distribution with lambda = 0.0678") + 
  xlab("Number of occurrences per day") + 
  ylab("Relative frequency") +
  geom_bar(aes(x=x_DV,y=y_DV/(365*4+1)), stat = "identity") +
  geom_line(aes(x=x_DV,y=fx), color='red') +
  geom_point(aes(x=x_DV,y=fx), color='red')

We can see that the Poisson distribution fits well with the histogram.

Next, we try to estimate \(99\%\) Confidence Interval of \(\lambda\). The variance of Poisson distribution is equal to its mean (\(\lambda\)). Therefore, \(99\%\) Confidence Interval of \(\lambda\) can be written as \[ \bar{x} - z_{*}\cdot\sqrt{\frac{\bar{x}}{n}} \leq \lambda \leq \bar{x} + z_{*}\cdot\sqrt{\frac{\bar{x}}{n}}, \] where \(\bar{x}\) is the sample mean, \(n\) is the sample size, and \(z_*\) is z-value corresponding to the \(99\%\) confidence interval, and the value is 2.58. From this expression, 99% Confidence Interval of \(\lambda\) for DV before COVID-19 is [0.05, 0.0856].

After COVID-19

The frequency table of DV after COVID-19 is as follows.

DF_WM_20_21 <- DF_WM[DF_WM$Arrest_Year%in%c(2020,2021),]
DF_WM_20_21_DV <- DF_WM_20_21[DF_WM_20_21$Arrest_Category=='Offenses Against Family & Children',]

# table of date and the number of occurrences
DV_day_20_21 <- sapply(unique(DF_WM_20_21_DV$Arrest_Date),
                       function(x){sum(DF_WM_20_21_DV$Arrest_Date==x)})
# of occurrences per day Frequency Relative frequency
0 680 0.9302326
1 47 0.0642955
2 1 0.001368
3 0 0
4 1 0.001368
5 0 0
… 0 0
44 0 0
45 1 0.001368
46 0 0
… 0 0
77 0 0
78 1 0.001368
79 0 0
… 0 0

There are two outliers (45 and 78) in the table. The dates of them are 1 and 1. Since these dates are correspond to “Capitol attack” and “George Floyd protests”, we will drop the value of these dates.

The calculated \(\lambda = 0.0725\). The histogram and the poisson distribution with \(\lambda = 0.0725\) are shown in Figure 16.

x_DV <- 0:5
y_DV <- c(680,47,1,0,1,0)
fx <- dpois(x=x_DV, lambda=53/(365*2+1))
data_DV <- data.frame(x_DV, y_DV, fx)

ggplot(data_DV, aes(x=x_DV,y=y_DV)) +
  ggtitle("Figure 15: Histogram of DV in 2020 - 2021") + 
  xlab("Number of occurrences per day") + 
  ylab("Frequency") +
  geom_bar(stat = "identity") 

ggplot(data_DV) +
  ggtitle("Figure 16: Reralive frequency histogram of DV in 2020 - 2021 \n and Pission distribution with lambda = 0.0725") + 
  xlab("Number of occurrences per day") + 
  ylab("Relative frequency") +
  geom_bar(aes(x=x_DV,y=y_DV/(365*2+1)), stat = "identity") +
  geom_line(aes(x=x_DV,y=fx), color='red') +
  geom_point(aes(x=x_DV,y=fx), color='red')

The Poisson distribution fits well with the histogram.

99% Confidence Interval of \(\lambda\) for DV after COVID-19 is [0.0465, 0.0985].

Comparing Confidence Intervals

Figure 17 shows the Confidence Intervals before and after COVID-19. There was overlap in the Confidence Intervals, and it is not possible to say that there was a change in the \(\lambda\) of “Offenses Against Family & Children” before or after COVID-19.

x <- c('Before COVID-19','After COVID-19')
pre_covid_interval <- c(99/(365*4+1)-2.58*(99/(365*4+1)/(356*4+1))**0.5, 99/(365*4+1)+ 2.58*(99/(365*4+1)/(356*4+1))**0.5)
post_covid_interval <- c(53/(365*2+1) - 2.58*(53/(365*2+1)/(356*2+1))**0.5, 53/(365*2+1) + 2.58*(53/(365*2+1)/(356*2+1))**0.5)
data_CI_DV <- data.frame(x,pre_covid_interval,post_covid_interval)

ggplot(data_CI_DV) +
  ggtitle("Figure 17: 99% Confidence Interval of lambda for DV") + 
  xlab("") +
  ylab("99% Confidence Interval of lambda") + 
  coord_flip() +
  geom_linerange(aes(x=x[1], ymin=pre_covid_interval[1], ymax=pre_covid_interval[2])) +
  geom_linerange(aes(x=x[2], ymin=post_covid_interval[1], ymax=post_covid_interval[2]))

Traffic Violations

Before COVID-19

The trend of “Traffic Violations” also appears to have changed after COVID-19. The frequency table of Traffic Violations before COVID-19 is as follows.

DF_WM_16_19_TV <- DF_WM_16_19[DF_WM_16_19$Arrest_Category=='Traffic Violations',]

# table of date and the number of occurrences
TV_day_16_19 <- sapply(unique(DF_WM_16_19_TV$Arrest_Date),
                       function(x){sum(DF_WM_16_19_TV$Arrest_Date==x)})
# of occurrences per day Frequency Relative frequency
0 602 0.4123288
1 530 0.3627652
2 225 0.1540041
3 77 0.0527036
4 22 0.0150582
5 4 0.0027379
6 1 6.844627^{-4}
7 0 0

The calculated \(\lambda = 0.907\). The histogram and the poisson distribution with \(\lambda = 0.907\) are shown in Figure 19.

x_TV <- 0:10
y_TV <- c(602,530,225,77,22,4,1,0,0,0,0)
fx <- dpois(x=x_TV, lambda=sum(TV_day_16_19)/(365*4+1))
data_TV <- data.frame(x_TV, y_TV, fx)

ggplot(data_TV, aes(x=x_TV,y=y_TV)) +
  ggtitle("Figure 18: Histogram of traffic violations in 2016 - 2019") + 
  xlab("Number of occurrences per day") + 
  ylab("Frequency") +
  geom_bar(stat = "identity") 

ggplot(data_TV) +
  ggtitle("Figure 19: Relative frequency histogram of traffic violations in 2016 - 2019 \n and Pission distribution with lambda = 0.907") + 
  xlab("Number of occurrences per day") + 
  ylab("Relative frequency") +
  geom_bar(aes(x=x_TV,y=y_TV/(365*4+1)), stat = "identity") +
  geom_line(aes(x=x_TV,y=fx), color="red") +
  geom_point(aes(x=x_TV,y=fx), color='red')

The Poisson distribution fits well with the histogram.

99% Confidence Interval of \(\lambda\) for Traffic Violations before COVID-19 is [0.842, 0.972].

After COVID-19

The frequency table of Traffic Violations after COVID-19 is as follows.

DF_WM_20_21_TV <- DF_WM_20_21[DF_WM_20_21$Arrest_Category=='Traffic Violations',]

# table of date and the number of occurrences
TV_day_20_21 <- sapply(unique(DF_WM_20_21_TV$Arrest_Date),
                       function(x){sum(DF_WM_20_21_TV$Arrest_Date==x)})
# of occurrences per day Frequency Relative frequency
0 546 0.746922
1 156 0.2134063
2 23 0.0314637
3 3 0.004104
4 3 0.004104
5 0 0

The calculated \(\lambda = 0.306\). The histogram and the poisson distribution with \(\lambda = 0.306\) are shown in Figure 21.

x_TV <- 0:10
y_TV <- c(546,156,23,3,3,0,0,0,0,0,0)
fx <- dpois(x=x_TV, lambda=sum(TV_day_20_21)/(365*2+1))
data_TV <- data.frame(x_TV, y_TV, fx)

ggplot(data_TV, aes(x=x_TV,y=y_TV)) +
  ggtitle("Figure 20: Histogram of traffic violations in 2020 - 2021") + 
  xlab("Number of occurrences per day") + 
  ylab("Frequency") +
  geom_bar(stat = "identity") 

ggplot(data_TV) +
  ggtitle("Figure 21: Relative frequency histogram of traffic violations in 2020 - 2021 \n and Pission distribution with lambda = 0.306") + 
  xlab("Number of occurrences per day") + 
  ylab("Relative frequency") +
  geom_bar(aes(x=x_TV,y=y_TV/(365*2+1)), stat = "identity") +
  geom_line(aes(x=x_TV,y=fx), color="red") +
  geom_point(aes(x=x_TV,y=fx), color='red')

The Poisson distribution fits well with the histogram.

99% Confidence Interval of \(\lambda\) for Traffic Violations before COVID-19 is [0.252, 0.358].

Comparing Confidence Intervals

Figure 22 shows the Confidence Intervals before and after COVID-19. There was no overlap in the Confidence Intervals, and there may have been a change in the Traffic Violations lambda before and after COVID-19.

x <- c('Before COVID-19','After COVID-19')
pre_covid_interval <- c(sum(TV_day_16_19)/(365*4+1) - 2.58*(sum(TV_day_16_19)/(365*4+1)/(356*4+1))**0.5,
                        sum(TV_day_16_19)/(365*4+1) + 2.58*(sum(TV_day_16_19)/(365*4+1)/(356*4+1))**0.5)
post_covid_interval <- c(sum(TV_day_20_21)/(365*2+1) - 2.58*(sum(TV_day_20_21)/(365*2+1)/(356*2+1))**0.5,
                         sum(TV_day_20_21)/(365*2+1) + 2.58*(sum(TV_day_20_21)/(365*2+1)/(356*2+1))**0.5)
data_CI_TV <- data.frame(x,pre_covid_interval,post_covid_interval)

ggplot(data_CI_TV) +
  ggtitle("Figure 22: 99% Confidence Interval of lambda for Traffic Violations") + 
  ylab("99% Confidence Interval of lambda") + 
  xlab("") +
  coord_flip() +
  geom_linerange(aes(x=x[1], ymin=pre_covid_interval[1], ymax=pre_covid_interval[2])) +
  geom_linerange(aes(x=x[2], ymin=post_covid_interval[1], ymax=post_covid_interval[2]))

Simple Assault

Before COVID-19

The below table shows the frequency and relative frequency of Simple Assault before COVID-19.

DF_WM_16_19_SA <- DF_WM_16_19[DF_WM_16_19$Arrest_Category=='Simple Assault',]

# table of date and the number of occurrences
SA_day_16_19 <- sapply(unique(DF_WM_16_19_SA$Arrest_Date),
                       function(x){sum(DF_WM_16_19_SA$Arrest_Date==x)})
# of occurrences per day Frequency Relative frequency
0 438 0.2997947
1 479 0.3278576
2 284 0.1943874
3 156 0.1067762
4 76 0.0520192
5 13 0.008898
6 8 0.0054757
7 4 0.0027379
8 1 6.844627^{-4}
9 2 0.0013689
10 0 0

We got \(\lambda = 1.36\) by calculating the average of occurrences per day.

x_SA <- 0:10
y_SA <- c(438,479,284,156,76,13,8,4,1,2,0)
fx <- dpois(x=x_SA, lambda=sum(SA_day_16_19)/(365*4+1))
data_SA <- data.frame(x_SA, y_SA, fx)

ggplot(data_SA, aes(x=x_SA,y=y_SA)) +
  ggtitle("Figure 23: Histogram of Simple Assault in 2016 - 2019") + 
  xlab("Number of occurrences per day") + 
  ylab("Frequency") +
  geom_bar(stat = "identity") 

ggplot(data_SA) +
  ggtitle("Figure 24: Relative frequency histogram of Simple Assault in 2016 - 2019 \n and Poisson distribution with lambda = 1.36") + 
  xlab("Number of occurrences per day") + 
  ylab("Relative frequency") +
  geom_bar(aes(x=x_SA,y=y_SA/(365*4+1)), stat = "identity") +
  geom_line(aes(x=x_SA,y=fx), color='red') +
  geom_point(aes(x=x_SA,y=fx), color='red')

After COVID-19

The frequency and relative frequency in 2020 and 2021 is shown in below. The \(\lambda\) for 2020 and 2021 was \(0.923\).

DF_WM_20_21_SA <- DF_WM_20_21[DF_WM_20_21$Arrest_Category=='Simple Assault',]

# table of date and the number of occurrences
SA_day_20_21 <- sapply(unique(DF_WM_20_21_SA$Arrest_Date),
                       function(x){sum(DF_WM_20_21_SA$Arrest_Date==x)})
# of occurrences per day Frequency Relative frequency
0 297 0.4062927
1 267 0.3652531
2 112 0.1532148
3 43 0.0588235
4 8 0.0109439
5 3 0.004104
6 0 0
7 0 0
8 1 0.001368
9 0 0 
x_SA <- 0:10
y_SA <- c(297,267,112,43,8,3,0,0,1,0,0)
fx <- dpois(x=x_SA, lambda=sum(SA_day_20_21)/(365*2+1))
data_SA <- data.frame(x_SA, y_SA, fx)

ggplot(data_SA, aes(x=x_SA,y=y_SA)) +
  ggtitle("Figure 25: Histogram of Simple Assault in 2020 - 2021") + 
  xlab("Number of occurrences per day") + 
  ylab("Frequency") +
  geom_bar(stat = "identity") 

ggplot(data_SA) +
  ggtitle("Figure 25: Relative frequency histogram of Simple Assault in 2020 - 2021 \n and Poisson distribution with lambda = 0.923") + 
  xlab("Number of occurrences per day") + 
  ylab("Relative frequency") +
  geom_bar(aes(x=x_SA,y=y_SA/(365*2+1)), stat = "identity") +
  geom_line(aes(x=x_SA,y=fx), color='red') +
  geom_point(aes(x=x_SA,y=fx), color='red')

Comparing Confidence Intervals

Figure 26 shows the Confidence Intervals before and after COVID-19. There was no overlap in the Confidence Intervals, and there may have been a change in the Simple Assault lambda before and after COVID-19.

x <- c('Before COVID-19','After COVID-19')
pre_covid_interval <- c(sum(SA_day_16_19)/(365*4+1) - 2.58*(sum(SA_day_16_19)/(365*4+1)/(356*4+1))**0.5,
                        sum(SA_day_16_19)/(365*4+1) + 2.58*(sum(SA_day_16_19)/(365*4+1)/(356*4+1))**0.5)
post_covid_interval <- c(sum(SA_day_20_21)/(365*2+1) - 2.58*(sum(SA_day_20_21)/(365*2+1)/(356*2+1))**0.5,
                         sum(SA_day_20_21)/(365*2+1) + 2.58*(sum(SA_day_20_21)/(365*2+1)/(356*2+1))**0.5)
data_CI_SA <- data.frame(x,pre_covid_interval,post_covid_interval)

ggplot(data_CI_SA) +
  ggtitle("Figure 26: 99% Confidence Interval of lambda for Simple Assault") + 
  ylab("99% Confidence Interval of lambda") + 
  xlab("") +
  coord_flip() +
  geom_linerange(aes(x=x[1], ymin=pre_covid_interval[1], ymax=pre_covid_interval[2])) +
  geom_linerange(aes(x=x[2], ymin=post_covid_interval[1], ymax=post_covid_interval[2]))

Theft

Before COVID-19

The frequency and relative frequency in 2016 to 2019 is shown in below. The \(\lambda\) before COVID-19 was \(0.404\).

DF_WM_16_19_T <- DF_WM_16_19[DF_WM_16_19$Arrest_Category=='Theft',]

# table of date and the number of occurrences
T_day_16_19 <- sapply(unique(DF_WM_16_19_T$Arrest_Date),
                       function(x){sum(DF_WM_16_19_T$Arrest_Date==x)})
# of occurrences per day Frequency Relative frequency
0 973 0.6659822
1 398 0.2724162
2 79 0.0540726
3 10 0.0068446
4 1 6.844627^{-4}
5 0 0 
x_T <- 0:5
y_T <- c(973,398,79,10,1,0)
fx <- dpois(x=x_T, lambda=sum(T_day_16_19)/(365*4+1))
data_T <- data.frame(x_T, y_T, fx)

ggplot(data_T, aes(x=x_T,y=y_T)) +
  ggtitle("Figure 27: Histogram of Theft in 2016 - 2019") + 
  xlab("Number of occurrences per day") + 
  ylab("Frequency") +
  geom_bar(stat = "identity") 

ggplot(data_T) +
  ggtitle("Figure 28: Relative frequency histogram of Theft in 2016 - 2019 \n and Poisson distribution with lambda = 0.404") + 
  xlab("Number of occurrences per day") + 
  ylab("Relative frequency") +
  geom_bar(aes(x=x_T,y=y_T/(365*4+1)), stat = "identity") +
  geom_line(aes(x=x_T,y=fx), color='red') +
  geom_point(aes(x=x_T,y=fx), color='red')

After COVID-19

The frequency and relative frequency in 2020 and 2021 are shown in below. The \(\lambda\) for 2020 and 2021 was \(0.115\).

DF_WM_20_21_T <- DF_WM_20_21[DF_WM_20_21$Arrest_Category=='Theft',]

# table of date and the number of occurrences
T_day_20_21 <- sapply(unique(DF_WM_20_21_T$Arrest_Date),
                       function(x){sum(DF_WM_20_21_T$Arrest_Date==x)})
# of occurrences per day Frequency Relative frequency
0 653 0.8932969
1 72 0.0984952
2 6 0.0082079
3 0 0 
x_T <- 0:3
y_T <- c(653,72,6,0)
fx <- dpois(x=x_T, lambda=sum(T_day_20_21)/(365*2+1))
data_T <- data.frame(x_T, y_T, fx)

ggplot(data_T, aes(x=x_T,y=y_T)) +
  ggtitle("Figure 29: Histogram of Theft in 2020 - 2021") + 
  xlab("Number of occurrences per day") + 
  ylab("Frequency") +
  geom_bar(stat = "identity") 

ggplot(data_T) +
  ggtitle("Figure 30: Relative frequency histogram of Theft in 2020 - 2021 \n and Poisson distribution with lambda = 0.115") + 
  xlab("Number of occurrences per day") + 
  ylab("Relative frequency") +
  geom_bar(aes(x=x_T,y=y_T/(365*2+1)), stat = "identity") +
  geom_line(aes(x=x_T,y=fx), color='red') +
  geom_point(aes(x=x_T,y=fx), color='red')

Comparing Confidence Intervals

Figure 31 shows the Confidence Intervals before and after COVID-19. There was no overlap in the Confidence Intervals, and there may have been a change in the Theft lambda before and after COVID-19.

x <- c('Before COVID-19','After COVID-19')
pre_covid_interval <- c(sum(T_day_16_19)/(365*4+1) - 2.58*(sum(T_day_16_19)/(365*4+1)/(356*4+1))**0.5,
                        sum(T_day_16_19)/(365*4+1) + 2.58*(sum(T_day_16_19)/(365*4+1)/(356*4+1))**0.5)
post_covid_interval <- c(sum(T_day_20_21)/(365*2+1) - 2.58*(sum(T_day_20_21)/(365*2+1)/(356*2+1))**0.5,
                         sum(T_day_20_21)/(365*2+1) + 2.58*(sum(T_day_20_21)/(365*2+1)/(356*2+1))**0.5)
data_CI_T <- data.frame(x,pre_covid_interval,post_covid_interval)

ggplot(data_CI_T) +
  ggtitle("Figure 31: 99% Confidence Interval of lambda for Theft") + 
  ylab("99% Confidence Interval of lambda") + 
  xlab("") +
  coord_flip() +
  geom_linerange(aes(x=x[1], ymin=pre_covid_interval[1], ymax=pre_covid_interval[2])) +
  geom_linerange(aes(x=x[2], ymin=post_covid_interval[1], ymax=post_covid_interval[2]))

Interpretation

Simple Assault and Traffic Violations

Statistically significant reductions in Simple Assault and Traffic Violations were observed for \(\lambda\) before and after COVID-19. Since these crimes seem to be more likely to occur the more people are out, it is likely that the restrictions and curbs on going out due to COVID-19 contributed to the decrease in these crimes.

Theft

A statistically significant decrease in theft was also observed in \(\lambda\) before and after Corona. Considering that thefts are committed against empty homes, the decrease in empty homes due to the curfew restrictions caused by COVID-19 may have contributed to the decrease in thefts.

Offenses Against Family & Children

The more time one spends at home due, the more Offenses Against Family & Children are likely to increase. In fact, in terms of the number of cases alone, Offenses Against Family & Children have increased after COVID-19. At first glance, the curfew restrictions caused by COVID-19 seems to be the cause. However, most of these cases were caused by special incidents unrelated to COVID-19, and when these effects were removed, there was no statistically significant difference in the change in Offenses Against Family & Children before and after COVID-19. As for white males in the DC area, Offenses Against Family & Children to the point of arrest does not appear to be affected by the changes in their lives caused by COVID-19.

Appendix - Other Major Crimes

Release Violations/Fugitive

Before COVID-19

DF_WM_16_19_RV <- DF_WM_16_19[DF_WM_16_19$Arrest_Category=='Release Violations/Fugitive',]

# table of date and the number of occurrences
RV_day_16_19 <- sapply(unique(DF_WM_16_19_RV$Arrest_Date),
                       function(x){sum(DF_WM_16_19_RV$Arrest_Date==x)})
# of occurrences per day Frequency Relative frequency
0 817 0.559206
1 428 0.29295
2 168 0.1149897
3 40 0.0273785
4 5 0.0034223
5 3 0.0020534
6 0 0 
x_RV <- 0:6
y_RV <- c(817,428,168,40,5,3,0)
fx <- dpois(x=x_RV, lambda=sum(RV_day_16_19)/(365*4+1))
data_RV <- data.frame(x_RV, y_RV, fx)

ggplot(data_RV, aes(x=x_RV,y=y_RV)) +
  ggtitle("Figure : Histogram of Release Violations/Fugitive in 2016 - 2019") + 
  xlab("Number of occurrences per day") + 
  ylab("Frequency") +
  geom_bar(stat = "identity") 

ggplot(data_RV) +
  ggtitle("Figure : Relative frequency histogram of Release Violations/Fugitive in 2016 - 2019 \n and Poisson distribution with lambda = 0.629") + 
  xlab("Number of occurrences per day") + 
  ylab("Relative frequency") +
  geom_bar(aes(x=x_RV,y=y_RV/(365*4+1)), stat = "identity") +
  geom_line(aes(x=x_RV,y=fx), color='red') +
  geom_point(aes(x=x_RV,y=fx), color='red')

After COVID-19

DF_WM_20_21_RV <- DF_WM_20_21[DF_WM_20_21$Arrest_Category=='Release Violations/Fugitive',]

# table of date and the number of occurrences
RV_day_20_21 <- sapply(unique(DF_WM_20_21_RV$Arrest_Date),
                       function(x){sum(DF_WM_20_21_RV$Arrest_Date==x)})
# of occurrences per day Frequency Relative frequency
0 549 0.751026
1 154 0.2106703
2 24 0.0328317
3 4 0.005472
4 0 0 
x_RV <- 0:4
y_RV <- c(549,154,24,4,0)
fx <- dpois(x=x_RV, lambda=sum(RV_day_20_21)/(365*2+1))
data_RV <- data.frame(x_RV, y_RV, fx)

ggplot(data_RV, aes(x=x_RV,y=y_RV)) +
  ggtitle("Figure : Histogram of Release Violations/Fugitive in 2020 - 2021") + 
  xlab("Number of occurrences per day") + 
  ylab("Frequency") +
  geom_bar(stat = "identity") 

ggplot(data_RV) +
  ggtitle("Figure : Relative frequency histogram of Release Violations/Fugitive in 2020 - 2021 \n and Poisson distribution with lambda = 0.293") + 
  xlab("Number of occurrences per day") + 
  ylab("Relative frequency") +
  geom_bar(aes(x=x_RV,y=y_RV/(365*2+1)), stat = "identity") +
  geom_line(aes(x=x_RV,y=fx), color='red') +
  geom_point(aes(x=x_RV,y=fx), color='red')

Comparing Confidence Intervals

x <- c('Before COVID-19','After COVID-19')
pre_covid_interval <- c(sum(RV_day_16_19)/(365*4+1) - 2.58*(sum(RV_day_16_19)/(365*4+1)/(356*4+1))**0.5,
                        sum(RV_day_16_19)/(365*4+1) + 2.58*(sum(RV_day_16_19)/(365*4+1)/(356*4+1))**0.5)
post_covid_interval <- c(sum(RV_day_20_21)/(365*2+1) - 2.58*(sum(RV_day_20_21)/(365*2+1)/(356*2+1))**0.5,
                         sum(RV_day_20_21)/(365*2+1) + 2.58*(sum(RV_day_20_21)/(365*2+1)/(356*2+1))**0.5)
data_CI_RV <- data.frame(x,pre_covid_interval,post_covid_interval)

ggplot(data_CI_RV) +
  ggtitle("Figure : 99% Confidence Interval of lambda for Release Violations/Fugitive") + 
  ylab("99% Confidence Interval of lambda") + 
  xlab("") +
  coord_flip() +
  geom_linerange(aes(x=x[1], ymin=pre_covid_interval[1], ymax=pre_covid_interval[2])) +
  geom_linerange(aes(x=x[2], ymin=post_covid_interval[1], ymax=post_covid_interval[2]))

Driving/Boating While Intoxicated

Before COVID-19

DF_WM_16_19_DI <- DF_WM_16_19[DF_WM_16_19$Arrest_Category=='Driving/Boating While Intoxicated',]

# table of date and the number of occurrences
DI_day_16_19 <- sapply(unique(DF_WM_16_19_DI$Arrest_Date),
                       function(x){sum(DF_WM_16_19_DI$Arrest_Date==x)})
# of occurrences per day Frequency Relative frequency
0 875 0.5989049
1 416 0.2847365
2 138 0.0944559
3 25 0.0171116
4 6 0.0041068
5 1 6.844627^{-4}
6 0 0 
x_DI <- 0:6
y_DI <- c(875,416,138,25,6,1,0)
fx <- dpois(x=x_DI, lambda=sum(DI_day_16_19)/(365*4+1))
data_DI <- data.frame(x_DI, y_DI, fx)

ggplot(data_DI, aes(x=x_DI,y=y_DI)) +
  ggtitle("Figure : Histogram of Driving/Boating While Intoxicated in 2016 - 2019") + 
  xlab("Number of occurrences per day") + 
  ylab("Frequency") +
  geom_bar(stat = "identity") 

ggplot(data_DI) +
  ggtitle("Figure : Relative frequency histogram of Driving/Boating While Intoxicated in 2016 - 2019 \n and Poisson distribution with lambda = 0.545") + 
  xlab("Number of occurrences per day") + 
  ylab("Relative frequency") +
  geom_bar(aes(x=x_DI,y=y_DI/(365*4+1)), stat = "identity") +
  geom_line(aes(x=x_DI,y=fx), color='red') +
  geom_point(aes(x=x_DI,y=fx), color='red')

After COVID-19

DF_WM_20_21_DI <- DF_WM_20_21[DF_WM_20_21$Arrest_Category=='Driving/Boating While Intoxicated',]

# table of date and the number of occurrences
DI_day_20_21 <- sapply(unique(DF_WM_20_21_DI$Arrest_Date),
                       function(x){sum(DF_WM_20_21_DI$Arrest_Date==x)})
# of occurrences per day Frequency Relative frequency
0 527 0.7209302
1 168 0.2298222
2 29 0.0396717
3 5 0.0068399
4 2 0.002736
5 0 0 
x_DI <- 0:5
y_DI <- c(527,168,29,5,2,0)
fx <- dpois(x=x_DI, lambda=sum(DI_day_20_21)/(365*2+1))
data_DI <- data.frame(x_DI, y_DI, fx)

ggplot(data_DI, aes(x=x_DI,y=y_DI)) +
  ggtitle("Figure : Histogram of Driving/Boating While Intoxicated in 2020 - 2021") + 
  xlab("Number of occurrences per day") + 
  ylab("Frequency") +
  geom_bar(stat = "identity") 

ggplot(data_DI) +
  ggtitle("Figure : Relative frequency histogram of Driving/Boating While Intoxicated in 2020 - 2021 \n and Poisson distribution with lambda = 0.341") + 
  xlab("Number of occurrences per day") + 
  ylab("Relative frequency") +
  geom_bar(aes(x=x_DI,y=y_DI/(365*2+1)), stat = "identity") +
  geom_line(aes(x=x_DI,y=fx), color='red') +
  geom_point(aes(x=x_DI,y=fx), color='red')

Comparing Confidence Intervals

x <- c('Before COVID-19','After COVID-19')
pre_covid_interval <- c(sum(DI_day_16_19)/(365*4+1) - 2.58*(sum(DI_day_16_19)/(365*4+1)/(356*4+1))**0.5,
                        sum(DI_day_16_19)/(365*4+1) + 2.58*(sum(DI_day_16_19)/(365*4+1)/(356*4+1))**0.5)
post_covid_interval <- c(sum(DI_day_20_21)/(365*2+1) - 2.58*(sum(DI_day_20_21)/(365*2+1)/(356*2+1))**0.5,
                         sum(DI_day_20_21)/(365*2+1) + 2.58*(sum(DI_day_20_21)/(365*2+1)/(356*2+1))**0.5)
data_CI_DI <- data.frame(x,pre_covid_interval,post_covid_interval)

ggplot(data_CI_DI) +
  ggtitle("Figure : 99% Confidence Interval of lambda for Driving/Boating While Intoxicated") + 
  ylab("99% Confidence Interval of lambda") + 
  xlab("") +
  coord_flip() +
  geom_linerange(aes(x=x[1], ymin=pre_covid_interval[1], ymax=pre_covid_interval[2])) +
  geom_linerange(aes(x=x[2], ymin=post_covid_interval[1], ymax=post_covid_interval[2]))

Narcotics

Before COVID-19

DF_WM_16_19_N <- DF_WM_16_19[DF_WM_16_19$Arrest_Category=='Narcotics',]

# table of date and the number of occurrences
N_day_16_19 <- sapply(unique(DF_WM_16_19_N$Arrest_Date),
                       function(x){sum(DF_WM_16_19_N$Arrest_Date==x)})
# of occurrences per day Frequency Relative frequency
0 1053 0.7207392
1 318 0.2176591
2 66 0.0451745
3 10 0.0068446
4 5 0.0034223
5 6 0.0041068
6 0 0
7 1 6.844627^{-4}
8 0 0
9 1 6.844627^{-4}
10 0 0
11 0 0
12 0 0
13 1 6.844627^{-4}
14 0 0 
x_N <- 0:14
y_N <- c(1053,318,66,10,5,6,0,1,0,1,0,0,0,1,0)
fx <- dpois(x=x_N, lambda=sum(N_day_16_19)/(365*4+1))
data_N <- data.frame(x_N, y_N, fx)

ggplot(data_N, aes(x=x_N,y=y_N)) +
  ggtitle("Figure : Histogram of Narcotics in 2016 - 2019") + 
  xlab("Number of occurrences per day") + 
  ylab("Frequency") +
  geom_bar(stat = "identity") 

ggplot(data_N) +
  ggtitle("Figure : Relative frequency histogram of Narcotics in 2016 - 2019 \n and Poisson distribution with lambda = 0.383") + 
  xlab("Number of occurrences per day") + 
  ylab("Relative frequency") +
  geom_bar(aes(x=x_N,y=y_N/(365*4+1)), stat = "identity") +
  geom_line(aes(x=x_N,y=fx), color='red') +
  geom_point(aes(x=x_N,y=fx), color='red')

After COVID-19

DF_WM_20_21_N <- DF_WM_20_21[DF_WM_20_21$Arrest_Category=='Narcotics',]

# table of date and the number of occurrences
N_day_20_21 <- sapply(unique(DF_WM_20_21_N$Arrest_Date),
                       function(x){sum(DF_WM_20_21_N$Arrest_Date==x)})
# of occurrences per day Frequency Relative frequency
0 652 0.8919289
1 66 0.0902873
2 10 0.0136799
3 3 0.004104
4 0 0 
x_N <- 0:4
y_N <- c(652,66,10,3,0)
fx <- dpois(x=x_N, lambda=sum(N_day_20_21)/(365*2+1))
data_N <- data.frame(x_N, y_N, fx)

ggplot(data_N, aes(x=x_N,y=y_N)) +
  ggtitle("Figure : Histogram of Narcotics in 2020 - 2021") + 
  xlab("Number of occurrences per day") + 
  ylab("Frequency") +
  geom_bar(stat = "identity") 

ggplot(data_N) +
  ggtitle("Figure : Relative frequency histogram of Narcotics in 2020 - 2021 \n and Poisson distribution with lambda = 0.13") + 
  xlab("Number of occurrences per day") + 
  ylab("Relative frequency") +
  geom_bar(aes(x=x_N,y=y_N/(365*2+1)), stat = "identity") +
  geom_line(aes(x=x_N,y=fx), color='red') +
  geom_point(aes(x=x_N,y=fx), color='red')

Comparing Confidence Intervals

x <- c('Before COVID-19','After COVID-19')
pre_covid_interval <- c(sum(N_day_16_19)/(365*4+1) - 2.58*(sum(N_day_16_19)/(365*4+1)/(356*4+1))**0.5,
                        sum(N_day_16_19)/(365*4+1) + 2.58*(sum(N_day_16_19)/(365*4+1)/(356*4+1))**0.5)
post_covid_interval <- c(sum(N_day_20_21)/(365*2+1) - 2.58*(sum(N_day_20_21)/(365*2+1)/(356*2+1))**0.5,
                         sum(N_day_20_21)/(365*2+1) + 2.58*(sum(N_day_20_21)/(365*2+1)/(356*2+1))**0.5)
data_CI_N <- data.frame(x,pre_covid_interval,post_covid_interval)

ggplot(data_CI_N) +
  ggtitle("Figure : 99% Confidence Interval of lambda for Narcotics") + 
  ylab("99% Confidence Interval of lambda") + 
  xlab("") +
  coord_flip() +
  geom_linerange(aes(x=x[1], ymin=pre_covid_interval[1], ymax=pre_covid_interval[2])) +
  geom_linerange(aes(x=x[2], ymin=post_covid_interval[1], ymax=post_covid_interval[2]))

Liquor Law Violations

Before COVID-19

DF_WM_16_19_LV <- DF_WM_16_19[DF_WM_16_19$Arrest_Category=='Liquor Law Violations',]

# table of date and the number of occurrences
LV_day_16_19 <- sapply(unique(DF_WM_16_19_LV$Arrest_Date),
                       function(x){sum(DF_WM_16_19_LV$Arrest_Date==x)})
# of occurrences per day Frequency Relative frequency
0 1090 0.7460643
1 259 0.1772758
2 76 0.0520192
3 32 0.0219028
4 3 0.0020534
5 1 6.844627^{-4}
6 0 0 
x_LV <- 0:6
y_LV <- c(1090,259,76,32,3,1,0)
fx <- dpois(x=x_LV, lambda=sum(LV_day_16_19)/(365*4+1))
data_LV <- data.frame(x_LV, y_LV, fx)

ggplot(data_LV, aes(x=x_LV,y=y_LV)) +
  ggtitle("Figure : Histogram of Liquor Law Violations in 2016 - 2019") + 
  xlab("Number of occurrences per day") + 
  ylab("Frequency") +
  geom_bar(stat = "identity") 

ggplot(data_LV) +
  ggtitle("Figure : Relative frequency histogram of Liquor Law Violations in 2016 - 2019 \n and Poisson distribution with lambda = 0.359") + 
  xlab("Number of occurrences per day") + 
  ylab("Relative frequency") +
  geom_bar(aes(x=x_LV,y=y_LV/(365*4+1)), stat = "identity") +
  geom_line(aes(x=x_LV,y=fx), color='red') +
  geom_point(aes(x=x_LV,y=fx), color='red')

After COVID-19

DF_WM_20_21_LV <- DF_WM_20_21[DF_WM_20_21$Arrest_Category=='Liquor Law Violations',]

# table of date and the number of occurrences
LV_day_20_21 <- sapply(unique(DF_WM_20_21_LV$Arrest_Date),
                       function(x){sum(DF_WM_20_21_LV$Arrest_Date==x)})
# of occurrences per day Frequency Relative frequency
0 699 0.9562244
1 27 0.0369357
2 4 0.005472
3 1 0.001368
4 0 0 
x_LV <- 0:4
y_LV <- c(699,27,4,1,0)
fx <- dpois(x=x_LV, lambda=sum(LV_day_20_21)/(365*2+1))
data_LV <- data.frame(x_LV, y_LV, fx)

ggplot(data_LV, aes(x=x_LV,y=y_LV)) +
  ggtitle("Figure : Histogram of Liquor Law Violations in 2020 - 2021") + 
  xlab("Number of occurrences per day") + 
  ylab("Frequency") +
  geom_bar(stat = "identity") 

ggplot(data_LV) +
  ggtitle("Figure : Relative frequency histogram of Liquor Law Violations in 2020 - 2021 \n and Poisson distribution with lambda = 0.052") + 
  xlab("Number of occurrences per day") + 
  ylab("Relative frequency") +
  geom_bar(aes(x=x_LV,y=y_LV/(365*2+1)), stat = "identity") +
  geom_line(aes(x=x_LV,y=fx), color='red') +
  geom_point(aes(x=x_LV,y=fx), color='red')

Comparing Confidence Intervals

x <- c('Before COVID-19','After COVID-19')
pre_covid_interval <- c(sum(LV_day_16_19)/(365*4+1) - 2.58*(sum(LV_day_16_19)/(365*4+1)/(356*4+1))**0.5,
                        sum(LV_day_16_19)/(365*4+1) + 2.58*(sum(LV_day_16_19)/(365*4+1)/(356*4+1))**0.5)
post_covid_interval <- c(sum(LV_day_20_21)/(365*2+1) - 2.58*(sum(LV_day_20_21)/(365*2+1)/(356*2+1))**0.5,
                         sum(LV_day_20_21)/(365*2+1) + 2.58*(sum(LV_day_20_21)/(365*2+1)/(356*2+1))**0.5)
data_CI_LV <- data.frame(x,pre_covid_interval,post_covid_interval)

ggplot(data_CI_LV) +
  ggtitle("Figure : 99% Confidence Interval of lambda for Liquor Law Violations") + 
  ylab("99% Confidence Interval of lambda") + 
  xlab("") +
  coord_flip() +
  geom_linerange(aes(x=x[1], ymin=pre_covid_interval[1], ymax=pre_covid_interval[2])) +
  geom_linerange(aes(x=x[2], ymin=post_covid_interval[1], ymax=post_covid_interval[2]))